Heat a pot of water to a boil for pasta. Salt boiling water and cook pasta to al dente. Heads up: reserve a ladle of the hot cooking water just before you drain pasta.
Place the frozen spinach on a plate and microwave to defrost it according to your microwave's directions. Place defrosted spinach in a clean kitchen towel and wring out the liquid.
Heat a deep skillet over medium-high heat. Add 2 tablespoons extra-virgin olive oil. Halve the zucchini lengthwise then thinly slice into half moons and add to the pan along with the mushrooms. Cook 2 to 3 minutes then add onions and garlic to the pan. Season the vegetables with salt and pepper. When the onions are tender, about 5 minutes, add defrosted spinach, separating into small bits as you handle it, and the roasted red peppers and toss to heat through. Transfer veggies to a dish and return skillet to stove top. Add remaining 1 tablespoon of extra-virgin olive oil and the butter. When the butter melts into extra-virgin olive oil, add 2 rounded tablespoons of flour and cook a minute or so, then whisk in stock and milk. Bring to a bubble and thicken the sauce, reducing it 2 to 3 minutes. Season the sauce with salt, pepper and nutmeg. Slide vegetables back into sauce.
Place the part-skim ricotta in a large shallow bowl and combine with a ladle of boiling, starchy pasta cooking water. Stir to combine then add in a couple of handfuls of grated cheese.
Drain pasta and toss with cheeses. Add half the vegetables and sauce to pasta and toss to combine. Tear or shred basil and toss into pasta. Adjust seasonings. Top bowlfuls of Vegetable Not-sagna with remaining veggies in sauce and pass extra grated cheese at the table.